Abstract
Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) :
3993-4017 This paper concerns the finite-time blow-up and asymptotic behaviour of
solutions to nonlinear Volterra integrodifferential equations. Our main
contribution is to determine sharp estimates on the growth rates of both
explosive and nonexplosive solutions for a class of equations with nonsingular
kernels under weak hypotheses on the nonlinearity. In this superlinear setting
we must be content with estimates of the form $\lim_{t\to\tau}A(x(t),t) = 1$,
where $\tau$ is the blow-up time if solutions are explosive or $\tau = \infty$
if solutions are global. Our estimates improve on the sharpness of results in
the literature and we also recover well-known blow-up criteria via new methods.